publication . Preprint . Article . 2012

Perturbed asymptotically linear problems

Rossella Bartolo; Anna Maria Candela; Addolorata Salvatore;
Open Access English
  • Published: 05 Jan 2012
Abstract
Comment: 13 pages
Subjects
free text keywords: Mathematics - Analysis of PDEs, 35J20, 58E05, Applied Mathematics, Infinity, media_common.quotation_subject, media_common, Omega, Bounded function, Topology, Continuous function, Mathematics, Asymptotically linear, Multiplicity (mathematics), Mathematical analysis
17 references, page 1 of 2

[1] H. Amann, E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa 7 (1980), 539-603.

[2] A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381. [OpenAIRE]

[3] P. Bartolo, V. Benci, D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity, Nonlinear Anal. 7 (1983), 981-1012. [OpenAIRE]

[4] V. Benci, On the critical point theory for indefinite functionals in the presence of symmetries, Trans. Am. Math. Soc. 274 (1982), 533-572. [OpenAIRE]

[5] V. Benci, A. Capozzi, D. Fortunato, Periodic solutions of Hamiltonian systems with superquadratic potential, Ann. Mat. Pura Appl. CXLIII (1986), 1-46.

[6] J. Cossio, S. Herr´on, C. V´elez, Existence of solutions for an asymptotically linear Dirichlet problem via Lazer-Solimini results, Nonlinear Anal. 71 (2009), 66-71.

[7] M. Degiovanni, S. Lancelotti, Perturbations of even nonsmooth functionals, Differential Integral Equations 8 (1995), 981-992. [OpenAIRE]

[8] M. Degiovanni, S. Lancelotti, Perturbations of critical values in nonsmooth critical point theory, in “Well-posed Problems and Stability in Optimization” (Y. Sonntag Ed.), Serdica Math. J. 22 (1996), 427-450. [OpenAIRE]

[9] M. Degiovanni, V. Raˇdulescu, Perturbations of nonsmooth symmetric nonlinear eigenvalue problems, C.R. Acad. Sci. Paris S´er. I 329 (1999), 281-286.

[10] M.A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Translated from the Russian edition, Moscow, 1956 (A.H. Armstrong, J. Burlak Eds), Pergamon, London; Macmillan, New York, 1964.

[11] N. Hirano, W. Zou, A perturbation method for multiple sign-changing solutions, Calc. Var. Partial Differential Equations 37 (2010), 87-98.

[12] S. Li, Z. Liu, Perturbations from symmetric elliptic boundary value problems, J. Differential Equations 185 (2002), 271-280.

[13] S. Li, Z. Liu, Multiplicity of solutions for some elliptic equations involving critical and supercritical Sobolev exponents, Topol. Methods Nonlinear Anal. 28 (2006), 235-261.

[14] J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York, 1989.

[15] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math. 65, Amer. Math. Soc., Providence, 1984.

17 references, page 1 of 2
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publication . Preprint . Article . 2012

Perturbed asymptotically linear problems

Rossella Bartolo; Anna Maria Candela; Addolorata Salvatore;